论文标题
nilpotent代数，隐式函数定理和多项式准群
Nilpotent algebras, implicit function theorem, and polynomial quasigroups
论文作者
论文摘要
我们研究有限的非缔合代数。我们证明了此类代数的隐式函数定理。这使我们能够本着这种代数和准群之间的对应关系，本着可划分无扭转的nilpotent群体和合理的nilpotent lie代数的经典对应的精神。我们研究了Nilpotent群体的同源物的相关问题，丝状含有最大溶解度长度的代数和部分有序的代数。
We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence between divisible torsion-free nilpotent groups and rational nilpotent Lie algebras. We study the related questions of the commensurators of nilpotent groups, filiform Lie algebras of maximal solvability length and partially ordered algebras.
